A company pays their employees $20 per hour. Using fractional notation, write a proportion that represents how long an employee must work to make $80. Use x to represent the unknown number of hours.
The proportion that represents how long an employee must work to make $80 is:
$\frac{x}{80} = \frac{1}{20}$.
This can also be written as:
$x/80 = 1/20$.
To write a proportion that represents how long an employee must work to make $80, we can set up the following equation:
$\frac{x}{80} = \frac{1}{20}$
In this equation, x represents the number of hours an employee must work, and 80 represents the amount of money they want to earn. Since the company pays $20 per hour, we set up the proportion by dividing the unknown value (x) by the desired amount of money ($80) and equating it to the fraction $\frac{1}{20}$.
To write a proportion that represents how long an employee must work to make $80, we can set up the proportion as follows:
$\frac{x}{80}=\frac{1}{20}$
Here's how we derived this proportion:
1. The unknown number of hours an employee needs to work is represented by the variable x.
2. To find the relationship between x and the amount earned, we compare it to the known hourly rate of $20.
3. Since an employee earns $20 for every hour worked, we can express this as the ratio 1:20 or $\frac{1}{20}$.
4. We set up the proportion by equating the ratio of x to the desired amount earned, $80, with the ratio of 1 to 20.
Now, to solve for x, we can cross-multiply and solve for x:
$\begin{align}
20x &= 80\\
x &= \frac{80}{20}\\
x &= 4
\end{align}$
Therefore, an employee must work for 4 hours to earn $80.